Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+y &= -1 \\ -9x+2y &= -1\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = 9x-1$ Divide both sides by $2$ to isolate $y$ $y = {\dfrac{9}{2}x - \dfrac{1}{2}}$ Substitute this expression for $y$ in the first equation. $-7x+({\dfrac{9}{2}x - \dfrac{1}{2}}) = -1$ $-7x + \dfrac{9}{2}x - \dfrac{1}{2} = -1$ Simplify by combining terms, then solve for $x$ $-\dfrac{5}{2}x - \dfrac{1}{2} = -1$ $-\dfrac{5}{2}x = -\dfrac{1}{2}$ $x = \dfrac{1}{5}$ Substitute $\dfrac{1}{5}$ for $x$ back into the top equation. $-7( \dfrac{1}{5})+y = -1$ $-\dfrac{7}{5}+y = -1$ $y = \dfrac{2}{5}$ $y = \dfrac{2}{5}$ The solution is $\enspace x = \dfrac{1}{5}, \enspace y = \dfrac{2}{5}$.